The present invention relates generally to a profile simulation method, and more particularly to a profile simulation method for forming an optimal resist pattern by estimating a variation in profile of a resist which is to be dissolved with a developer when a semiconductor device, etc. is manufactured by a lithography process, as well as a storage medium storing a program for carrying out the profile simulation method.
In a method of fabricating a semiconductor device, etc. by a lithography process, an image of a mask pattern is projected on a resist (photosensitive film) coated on a wafer and the image on the resist on the wafer is developed. For example, when the resist is of a positive type, a portion of the resist, which has been exposed to light to a greater degree, is dissolved with a developer and a resist pattern is formed.
The developed resist pattern varies depending on the focusing/defocusing state of a mask pattern image projected on the wafer, conditions for exposure (numerical aperture, coherence factor, shape of light source, pupil filter, etc.), a development time, the mask pattern itself, etc. Thus, a great number of experiments of exposure need to be conducted to find the conditions of the optical projecting system for producing a desired pattern with a predetermined focal depth and to find a mask pattern.
It is thus desirable to find, by computer simulation, the conditions in advance, under which an optimal resist profile will be developed. A method for estimating a developed resist profile is known as resist profile simulation, which will now be described.
When a two-dimensional profile alone is treated, a resist profile is expressed by a succession of minute line segments. When a three-dimensional profile is treated, a resist profile is expressed by a succession of minute plane segments. The direction of movement of the minute line segment or minute plane segment is set to be perpendicular to the surface of the resist. This technique is called "string model." On the other hand, in "ray tracing model", the direction of movement is found by a differential equations similar to those for light rays.
In addition, a method called "cell model" is known, wherein an object is divided into a group of small cells, and a variation in profile is expressed by deletion or addition of cells on the surface of the object. Moreover, there is known a distribution function method wherein the profile of an object is expressed by equivalent faces of a distribution function and a time-basis variation of the profile is found by solving a differential equation similar to a diffusion equation.
Besides, there is known a simplified development model wherein a point on a resist surface, where a dissolution rate is highest in a development process, is set as a start position and it is supposed that development progresses in a direction perpendicular to the substrate and then progresses in a direction parallel to the substrate and that the change in direction of development occurs at any point perpendicular to the substrate. According to this method, the profile of a developed resist is estimated on the basis of a group of end points.
However, the above methods have the following problems. In the prior art, the dissolution rate of a resist depends only on the exposure, photosensitivity characteristics of the resist and process conditions, or, in addition to these, the profile of a dissolved portion of the resist.
For example, when an isolated pattern portion and a dense pattern portion are coexisting, the concentration of a reaction product of a resist dissolved in a developer, that is, the OH.sup.- concentration in the developer, varies between a region near the isolated pattern portion and a region near the dense pattern portion. Consequently, the dimensions of a finished isolated pattern portion and those of a finished dense pattern portion cannot exactly be estimated at the same time.
As has been described above, various simulation methods have been proposed to estimate a resist pattern profile. In each method, it is not possible to exactly estimate the dimensions of a finished isolated pattern portion and those of a finished dense pattern portion at the same time. This problem arises not only in the case of forming a resist pattern but also in the case of treating a film by means of etching, etc.